Combining the Distribution of Relaxation Times from EIS and Time-Domain Data for Parameterizing Equivalent Circuit Models of Lithium-Ion Batteries

Abstract

Equivalent circuit models (ECMs) are a widely used modeling approach for lithium-ion batteries in engineering applications. The RC elements, which display the dynamic loss processes of the cell, are usually parameterized by fitting the ECM to experimental data in either the time-domain or the frequency-domain. However, both types of data have limitations with regard to the observable time constants of electrochemical processes. This work proposes a method to combine time-domain and frequency-domain measurement data for parameterization of RC elements by exploiting the full potential of the distribution of relaxation times (DRT). Instead of using only partial information from the DRT to supplement a conventional fitting algorithm, we determine the parameters of an arbitrary number of RC elements directly from the DRT. The difficulties of automated deconvolution of the DRT, including regularization and the choice of an optimal regularization factor, is tackled by using the L-curve criterion for optimized calculation of the DRT via Tikhonov regularization. Three different approaches to merge time- and frequency-domain data are presented, including a novel approach where the DRT is simultaneously calculated from electrochemical impedance spectoscropy (EIS) and pulse relaxation measurements. The parameterized model for a commercial 18650 NCA cell was validated during a validation cycle consisting of constant current and real-world automotive cycling and yields a relative improvement of over 40% compared to a conventional EIS-fitting algorithm.

Keywords

• lithium-ion batteries
• equivalent circuit model
• electrochemical impedance spectroscopy
• distribution of relaxation times
• Tikhonov regularization